How much energy must be transferred to raise the temperature of a cup of coffee (250 mL) from 20.5 C (293.7 K) to 95.6 C (368.8 K)? Assume that water and coffee have the same density (1.00 g/ mL), and specific heat capacity 4.184 J/ gK)?

Sep 15, 2016

The energy required is 77.5 kJ.

Explanation:

The energy required to heat an object is given by the formula

color(blue)(bar(ul(|color(white)(a/a)q = mcΔTcolor(white)(a/a)|)))" "

where

$q$ is the energy required
$m$ is the mass
$c$ is the specific heat capacity
ΔT is the change in temperature

m = 250 color(red)(cancel(color(black)("mL"))) × "1.00 g"/(1 color(red)(cancel(color(black)("mL")))) = "250 g"
$c = \text{4.184 J·K"^"-1"·"g"^"-1}$
ΔT = "368.8 K - 293.7 K = 74.1 K"
$q = \text{250" color(red)(cancel(color(black)("g"))) × "4.184 J"·color(red)(cancel(color(black)("K"^"-1"·"g"^"-1"))) × 74.1 color(red)(cancel(color(black)("K"))) = "77 500 J" = "77.5 kJ}$